8. If a population doubles every 5 years, how many years will it take for the population to increase by 10 times
its original amount?
First: If the population gets multiplied by 2 every 5 years, what does it get multiplied by each year? Use this
to help you answer the question.

Answer:

b = 4A-a-c-d

Step-by-step explanation:

A = (a+b+c+d)/4 |*4

4A = a+b+c+d |-a-c-d

4A-a-c-d = b

Store´s B bottle cost less per ounce.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Store A  

Cost of a 8-ounce bottle of water: $14

Store B

Cost of bottle: y= 1.5x

Cost per ounce (A)

=$14/ 8

= $1.75per ounce

Cost per ounce (B); $1.5 per ounce

So, $1.75 > $1.5

Hence, Store´s B bottle cost less per ounce.

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The solution set for the given quadratic equation is (-0.62, -5.38).

The given equation is 3x(x+6)=-10.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, 3x(x+6)=-10

⇒ 3x²+18x=-10

⇒ 3x²+18x+10=0

By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get

a=3, b=18 and c=10

Using quadratic formula x = [-b ± √(b² - 4ac)]/2a

= [-18 ± √(18² - 4×3×10)]/2×3

= [-18 ± √(324 - 120)]/6

= [-18 ± √(204)]/6

= [-18 ± √(204)]/6

= [-18 ± 14.28]/6

= [-18 + 14.28]/6 and [-18 - 14.28]/6

= -0.62 and -5.38

Hence, the solution set for the given quadratic equation is (-0.62, -5.38).

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Answer:

Step-by-step explanation:

We can observe:

According to  Hınge theorem if two sides of different triangles are equal and the angles between the two sides are different, then the larger angles has greater side opposite to it.

As TU is opposite to the larger angle, and SV is opposite to smaller angle, then TU > SV.

Correct angle choice is B.

Answer:

D

Step-by-step explanation:

In accordance to Thales's theorem, the geometric system has a missing side length of 15 units.

In this problem we find a geometric system formed by two proportional trapezoids. This similarity and proportionality is defined by Thales's theorem, which states that a triangle segmented by several lines parallel to each other and parallel to the base of the figure creates triangles and quadrilaterals proportional to each other.

Then, two figures of the given trapezoids are represented by side proportionality ratios. Then, the proportionality ratio is described and its variable x is cleared within by algebra properties:

First, define the proportionality ratio associated to the geometric system:

4 / (10 + 4) = (21 - x) / 21

Second, simplify the equation and clear the variable x:

4 / 14 = 1 - x / 21

2 / 7 = 1 - x / 21

42 / 7 = 21 - x

6 = 21 - x

x = 21 - 6

x = 15

The missing length is equal to 15 units.

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Answer:

115.226337449

Step-by-step explanation:

84/0.729= 115.226337449

And thank you and your welcome

Answer:  the quotient of 84/0.729 is 115.226337

The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

From the table

The investment in 1 year = $20000

The investment in 2 year = $21750

The investment in 3 year = $23500

The investment in 4 year = $25250

The investment in 5 year = $27000

Then the equation will be

y = 20000 + 1750x

Where y is the investment in dollars

x is the number of years

Draw the graph as number of years in x axis and the amount of investment in y axis

Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

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The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV

we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for  quadrant 2 and 3). Since we know cos² a + sin² a = 1

for α, cos² α + sin² α = 1

=> cos² α = 1 - sin² α

=> cos² α = 1 - 4/25

=> cos α = √21/25

same for β, cos² β + sin² β = 1

=> sin² β = 1 -cos² β

=> sin² β = 1 -1/9

= 8/9

=2√2/3

substituting the known values in the above formula for cos (α+β)

=>cos α cos β - sin α sin β

=√21/25 *1/3- 2/5*2√2/3

=√21/25- 4√2/15

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Answer:

d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]

Step-by-step explanation:

The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!

Have a lovely day!

Answer:

x = -12

Step-by-step explanation:

x/-3 + 5 - 5 = 9 - 5

x/-3 = 4

x/-3 (-3) = 4(-3)

x = -12

x - intercept is at ( 1, 0 ) graph intersect at x = 1 .

What are intercepts?

Domain - values of x on  x -axis taken by function

                - ( 0,5 )

Range = values of y on  y -axis taken by function

          = (-  ∞ , 2 )

           = ( as, x ⇒ 0 then graph goes below

b) x - intercept is at ( 1, 0 ) graph intersect at x = 1

          no y - intercept is there .

c) graph is not symmetric .

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The point (-2,7) is not lie on the graph of y = -2x +1 .

Given,

In the question:
To check the :

Does the point (-2, 7) lie on the graph of y=-2x+1?

Now, According to the question:

The equation is :

y = -2x + 1

Substitute the values of x = -2 and y = 7 into y = -2x +1

7 = -2(-2) + 1

LHS = 7

RHS = -2(-2) + 1 = 5

Write in the form :

7 = 5

Verify the relationship

False

Determine whether the point is on the line:
(-2, 7) not on the graph.

Hence, The point (-2,7) is not lie on the graph of y = -2x +1 .

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The smallest positive integer n will be 10 .

To find : the smallest positive integer n such that the rightmost digits of  n ! and ( n + 1 ) ! are same .

Since ,

putting n = 10 gives

n ! = 10 ! = 3628800

and ( n + 1 ) ! = 39916800

Last three digits ( rightmost digits ) ie. 800 are same .

Hence , n = 10 is the required answer ,

Therefore , the smallest positive integer is n = 10 such that the rightmost digits of  n ! and ( n + 1 ) ! are same .

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Answer:   14.4g of onion powder

Step-by-step explanation:   To get 20% of a number, you need to divide the original amount by 5, so 72 ÷5 is 14.4g

They should include 14.4 grams of onion powder in a bottle.

Given that, a seasoning blend is 4% onion powder, by mass.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let x be the seasoning blend.

Now, 4% of 72=20% of x

⇒ 0.04×72=0.2×x

⇒ 0.2x=2.88

⇒ x=2.88/0.2

⇒ x=14.4 g

Hence, they should include 14.4 grams of onion powder in a bottle.

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The answer is 3/25π m/h.

acc to our question-

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

hence,The answer is 3/25π m/h.

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Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.

Here,

A parallelogram has adjacent angles that add up to 180 degrees.

Since one angle of parallelogram is 120°.

240+2x=360

2x=120

x=60

The other will be 60°

The area of parallelogram= lh

l=15 inch

h=b(sin 60°)

=8*√3/2

h=4√3 inch

area of parallelogram= 15*4√3

= 60√3 inch²

The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."

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The greatest number of outfits Jose can buy is 6

The given parameters are:

Let the number of new biking outfits be x

So, we have

New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget

This gives

284.52 + 4  * 15.65 + 11.31 + 31.95x ≤ 580

This gives

358.43 + 31.95x ≤ 580

Solve the inequality

31.95x ≤ 221.57

Divide

x ≤ 6.93

This gives

x ≤ 6

Hence, the greatest number of outfits is 6

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The number of ways which are there to seat four of a group of ten people around a circular table is 1260.

To choose 4 people from a group of ten we need to count such people, which can be found using 10! / 4! × (10-4)! ,  after solving this we need to multiply 3! by this to get the desired answer. This is done because for that 4 people to sit in a circle, the possibilities for n people to sit around a circle is (n-1)! , and since n here is 4 the possibilities will also be (4-1)! which is 3! here.

Hence the final answer: 3! × 10! / 4! × (10-4)! = 1260

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There is a 0.48 percent chance that your phone will not be found and will therefore be stolen.

Let P(S|L) represent the likelihood that your phone was stolen if you left it in the computer lab.

Let P(S|C) indicate the likelihood that your phone was stolen if you left it at the cafe.

The likelihood that your phone will be stolen can be determined using law of total probability by:

P(S) = P(S|L)P(L) + P(S|C)P(C)

      = 0.3 * 0.4 + 0.6 * 0.6

      = 0.12 + 0.36

P(S) = 0.48

Therefore, there is a 0.48 percent chance that you won't find your phone and that it was stolen.

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The probability of choosing 3 men and 3 women to form the committee is 0.4329 and the probability to select exactly 2 people from the human resources is 0.4545.

It is given that there are 12 employees.

The number of male employees is 6

number of female employees is 6

A committee of 6 is to be formed. We need to find the probability that out of 6, 3 are male and 3 are female.

Let A be the event of having 3 men and 3 women on the committee

The total number of ways to choose 6 people is

¹²C₆

Probability = number of favorable outcomes / total number of outcomes

n(A) = ⁶C₃   X  ⁶C₃

Therefore,

P(A) = (⁶C₃   X  ⁶C₃) / ¹²C₆

= (20  X  20) / 924

= 400/924

= 0.4329

It is given that the number of employees in human resources from the group is 4

Let B be the event to choose exactly 2 employees from the human resource

n(B) = ⁴C₂  X  ⁸C₄

P(B) = ⁴C₂  X  ⁸C₄ / ¹²C₆

= 6 X 70 / 924

= 420 / 924

= 0.4545

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Answer:

-30

Step-by-step explanation:

Distribute

5 x -4= -20 2 x -2= -4

-20+(-6)+(-4)

Add together

-20 + -6= -26

-26 + (-4)

Add again

-26 + -4= -30

-30

Answer:

After 8 minutes ; altitude = 22,400 feet

Step-by-step explanation:

s1 = 2800t

s2 = -3200t + 48 000

2800t = -3200t + 48 000

28t = -32t + 480

7t = -8t + 120

7t + 8t = 120

15t = 120

15/15 t = 120/15

t = 8 minutes

s = 8 * (2800)  =   22400 feet

Answer:

(C.) 5/13

Step-by-step explanation:

The sine proportion is opposite / hypotenuse

Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse

Thus, sine is 5/13

The factor of the polynomial f(x) graphed on the coordinate plane is

(x - 1).

What is factor of the polynomial?

A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.

A polynomial can be factored by expressing it as the product of two or more components; this is somewhat the opposite of multiplying.

From the given graph we can see that, graph crosses x - axis at points

x = 1 and x = 8.

That means x = 1, 8 are the zero of the polynomial.

Since, if x = a is a zero of the polynomial, then (x - a) is the factor of the polynomial.

As x = 1, 8 are zero of the polynomial so (x - 1) and (x - 8) are the factors of the polynomial.

Hence, from the given options (x - 1) is factor of the polynomial.

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The cluster sample represents the the characteristic of group of same types objects.

What is the cluster sampling?

A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.

A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.

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The histogram that shows a left-skewed distribution is given by:

A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3).

An histogram is a graph that shows the number of times each element x was observed on the data-set.

Hence, the meaning of a point (x,y) on the histogram is given as follows:

Observation x was observed y times on the data-set.

The skewness of a distribution can be explained as follows:

Hence in this problem, for the left-skewed histogram, we want an "increasing" histogram, hence option A is correct.

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